Final answer:
Working backward from the third day, when the student had $40 left, calculations reveal that the student spent $75 on the second day, which was $5 plus 2/5 of what was left after Day 1. On Day 1, the student spent $2 plus 3/10 of their original amount, which is found to be $110 through backward calculations.
Step-by-step explanation:
To find out how much money the student originally had, we need to work backwards from the third day. Let's denote the original sum as x dollars.
Day 3
The student has $40 left. This means that after spending on Day 2, they were left with $40.
Day 2
The student spends $5 plus 2/5 of the rest. Let's call the remaining money after Day 1 y. So, the equation for Day 2's spending is $5 + 2/5(y). After spending, they are left with $40, so we can write:
y - (5 + 2/5(y)) = 40
Now let's solve for y:
y - 5 - 2/5(y) = 40
5/5(y) - 2/5(y) = 40 + 5
3/5(y) = 45
y = 45 / (3/5)
y = 45 * 5/3
y = 75
Thus, the student had $75 remaining at the beginning of Day 2.
Day 1
The student spends $2 plus 3/10 of the original sum. So, the money left after Day 1 spending would be:
x - (2 + 3/10(x)) = y
Substitute $75 for y:
x - 2 - 3/10(x) = 75
10/10(x) - 3/10(x) = 75 + 2
7/10(x) = 77
x = 77 / (7/10)
x = 77 * 10/7
x = 110
Thus, the student originally had $110.